Unparent object but keep animated properties
You can do this by baking the keyframes. This will overwrite the current keyframes of the child object and replace them with keyframes of both its own animation and the parent animation combined, so it retains the same movement but without having to be parented.

Select the object and choose Object> Animation> Bake Action. Set the range of the animation to bake, the Frame Step (to insert a keyframe on every nth frame) and enable Clear Parents (for some reason, for your example you also have to enable Visual Keying to get it to work correctly). After that you can click 'OK' to bake.



The baking process will then begin (which could be time consuming depending on the range of the animation and the Frame Step value).